2011-03-30
10:15 at HCI J 574

Linear stability of nonlinear waves in rarefied plasmas

Evangelos Siminos

Département de Physique Théorique et Appliquée, CEA - France

Kinetic effects in rarefied plasmas can be modeled by Boltzmann's equation coupled to macroscopic electromagnetic fields described by Maxwell's equations. In many situations of interest, including space and fusion plasmas, one may focus on long-range interactions and ignore collisional effects in the Boltzmann equation, which leads to the so-called Vlasov-Maxwell system. Despite the effort put in the theoretical understanding and numerical simulation of the Vlasov-Maxwell system, many fundamental issues remain unresolved. An outstanding issue of crucial importance to current inertial confinement fusion efforts is that of stability of nonlinear waves. Here we restrict attention to spatially periodic, nonlinear electrostatic waves in one spatial dimension (governed by the Vlasov equation and Poisson's law). We study the stability problem as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension. The Hermite expansion can be thought of as a formal moment expansion with no imposed closure. However, projection onto a finite dimensional system faces fundamental difficulties due to the Hamiltonian structure, long-range interactions, extreme range of scales and continuous linear spectrum in the Vlasov-Poisson system. These difficulties were resolved in our study using an operator-theoretic technique (spectral deformation), which establishes a formal connection to dissipative systems and suppresses non-essential scales. This formulation allows the determination of the unstable eigenmodes of a Vlasov equilibrium and illuminates the physical mechanism underlying the instability. As an example application, I will present a vortex-fusion instability scenario, of importance to the saturation of nonlinear processes in laser-plasma interaction.